Moiré artifacts and other forms of aliasing often appear in electronic imaging systems due to insufficient sampling of the optical images. Spatial aliasing occurs when the optical image bandwidth exceeds that of the image detector. Spatial aliasing manifests itself when a TV host wears a fine-striped shirt, producing distracting moirés.

George's moirés

George's moirés

Temporal aliasing occurs when the temporal bandwidth of the imaged scene exceeds the frame rate of the camera. Temporal aliasing manifests itself in the wagon wheel illusion in a Western movie. A rotating wagon wheel will appear to freeze or even to reverse its rotation.

Why don’t biological systems experience aliasing — or do they? Does the eye or brain circuits exhibit aliasing and moiré phenomena?

The human eye appears to avoid spatial aliasing by supersampling the optical signal: the point spread function of the eye optics covers several photoreceptors. What limits the resolution of the eye is the optics. The cornea, aqueous humor, the lens, vitrous humor, and three layers of retinal cells in front of the photoreceptors blur the signal and efficiently remove the very high-frequency content in the image. In addition, the arrangement of photoreceptors is not strictly regular as happens in a CCD chip for example. Thus chances of producing a spatial moiré pattern in the eye are nil.

However, temporal or spatiotemporal aliasing may occur, probably in motion processing areas of the visual cortex. One manifestation of this glitch is the motion reversal illusion sometimes perceived when a spoked wheel accelerates and decelerates through a range of RPMs. Skeptical that this could be the result of the stroboscopic effect of electric lighting, I made a black-and-white pinwheel and spun it. Even in daylight, at some rotation rates, I perceived subtle and transient episodes of illusory reversal. You can try this for yourself.

I spun this wheel to reproduce the rotation reversal illusion.

Spinning wheel to reproduce the rotation reversal illusion.

Is this evidence that the visual system has a semi-regular ‘frame rate’ similar to video and film cameras? I found it hard to believe. Temporally subsampled signals indicate inefficiencies undercutting the quantum efficiency (ie overall sensitivity) of the system, a problem that’s too easily fixed by introducing additional blurring (low-pass filtering) to limit the bandwidth before sampling. Temporal blurring is something very easy for cells to do and evolution would have long found a way to blur the signal, even if vision did work in regular discontinuous frames. There has to be something else to account for the illusory motion reversal.

In a recent paper by Kline and Eagleman (2008) in the Journal of Vision titled “Evidence against the snapshot hypothesis of illusory motion reversal”, the authors staged a series of experiments that argued against the snapshot hypothesis (frame-rate hypothesis).
The experiments support the rivalry hypothesis of the illusory motion reversal, ie that “the continuous stimulation of one direction of motion eventually causes rivalry with the opposite direction of motion, and the balance of the rivalry eventually tips, engendering the perception of reversed motion”. In other words, motion detection is hypothesized to consist of multiple motion detectors that each have undersampled spatiotemporal responses, many of which produce aliasing. Normally, those motion detectors that detect correct motion are stimulated stronger than their aliased counterparts resulting in correct perception. However, in continuous exposure, the strongly stimulated detectors desensitize and the aliased detectors get their opinions heard. That’s the putative mechanism, but no specific circuits responsible for this illusion have yet been described.

Monstein moiré


I have just posted a video of a moiré pattern I generated earlier


The two gratings encrypt the images of Albert Einstein and Mona Lisa, hence Monstein. The two gratings are in green and purple — two opposite colors to combine into a gray image.

Here are some online applications that let you play with moiré patterns:

1. Project LITE at Boston University
2. Elisabeth Sylvan student project at MIT
3. Moire videos at phidelity blog
4. iMoire by Vincent Scheib

A common misconception of shadows is that they must be binary, producing images comprising only black and white areas.

The following figures are adapted (with some conceptual changes) from a patent application I filed while employed at General Electric (US 20080037709A1: METHOD AND SYSTEM FOR CONTROLLING RADIATION INTENSITY OF AN IMAGING SYSTEM). The invention uses shadows from superposed opaque gratings to control the spatial distribution of x-ray radiation intensities in an x-ray beam.

First, we produce two gratings comprising curved opaque bars:

Then, we superpose them with some distance separating them and shine light through them at different angles as shown:

The bars are curved so that the same two gratings together cast shadows containing two different detailed images (not just contours):

Yet, this is not the whole story. If the light comes not from a point source but from a somewhat diffuse source (e.g. the sun), then the shadow will be blurred somewhat by penumbra or half-shadows producing a full-grayscale image:

The blur removes the sharp edges and, paradoxically, improves the images. Notice for example the wrinkles on Albert’s face that only come through after the images has been blurred.

Another way to achieve blurring is to rapidly shake the gratings perpendicularly to the bars. Motion blur will then remove the sharp edges from the image producing a similarly smooth image.

You can print the gratings in (a) and (b) on transparencies and superpose them with slight offsets to see the effect for yourselves.

What if such gratings are built as sculpture pieces or are integrated into the facade of a building or as sundials that would cast various artistic shadows at various times of the day at various seasons? What do you think?

Moirés in architecture can add a sense of motion to the building. As you walk past the building, the pattern will appear to move and dance – I can almost see it.

Such patterns could be dramatically improved by using color, generating meaningful images instead of simple geometric patterns, and making the patterns vary with the position of the sun.